the sun - Given a date obtain latitude and longitude where is the sun zenith

Searching is easy to find terminator line (frontier between day and night) or the position of the sun in the sky given a position on the earth and a time; but I can't find how to obtain where is the zenith of the sun given a date (and time).

I need to obtain the center of the illuminated zone of the earth (latitude and longitude) at a given time. (Well, actually I need the opposite, the Nadir, but with one you can calculate easily the other).

Any knows the function?

Thank you.